Chapter 7

length of intercepted arc is:

(s)= r(theta angle)

Unit Circle: what is the radians when it is at every 60 degrees?

(some even number, goes by 2, then 4)pie/3

Unit Circle: what is the radians for 180 degrees?

(some number, odd or even) (pie)

Which trig functions are negative in the 3rd quadrant?

- sin & (csc) - cos & (sec)

Which trig functions are negative in the 4th quadrant?

- sin & (csc) - tan & (cot)

Unit Circle: on the unit circle, x= ________ and y=____________

- x= cos - y=sin (tan= y/x, AKA sin/cos)

How can you remember which trig functions are positive in which quadrant?

-ALL (all trig functions are positive in the first quadrant) -STUDENTS (sin and csc are positive in the second quadrant) -TAKE (tan and cot are positive in the third quadrant) -CALCULUS (cos and sec are positive in the fourth quadrant) -go counterclockwise (1st, 2nd, 3rd, 4th quadrant) -if the trig functions aren't positive in a certain quadrant, then they are negative in that quadrant.

Which trig functions are negative in the 1st quadrant?

-NONE , they are all positive in the first quadrant

What does S stand for?

-basically the circumference -is the arc length

Which trig functions are positive in the 4th quadrant?

-cos -sec -basically cos and its reciprocal identity

Which trig functions are negative in the 2nd quadrant?

-cos & (sec) -tan & (cot)

how to convert a degree into radians

-degree times pie/180 degrees -make sure calculator is in radian mode

Unit Circle: there will be a 30 degree, 45 degree, 60 degree, and 90 degree in every __________

-in every quadrant of the unit circle (there are 4 quadrants in total)

how to convert radians into a degree

-radian times 180 degrees/pie -make sure calculator is in degree mode

Which trig functions are positive in the 2nd quadrant?

-sin -csc -basically sin and its reciprocal identity

Which trig functions are positive in the 1st quadrant?

-sin, cos, tan, csc, sec, cot -ALL OF THE SIGNS ARE POSITIVE IN THE FIRST QUADRANT

Which trig functions are positive in the 3rd quadrant?

-tan -cot -basically tan and its reciprocal identity

Unit Circle: what is cos at every 90 degrees?

0

Unit Circle: what is sin every 180 degrees?

0

Unit Circle: what is tan every 180 degrees?

0

Unit Circle: what is tan every 45 degrees?

1

Unit Circle: what is cos every 180 degrees?

1 (positive or negative depending on which quadrant)

Unit Circle: what is sin at every 90 degrees?

1 (positive or negative depending on which quadrant)

Unit Circle: what is sin every 30 degrees?

1/2 (positive or negative depending on which quadrant it is in)

Unit Circle: cos at every 60 degrees

1/2 (will be positive or negative depending on what quadrant it is in)

1 degree= how many seconds?''

3600''

1 degree= how many minutes?'

60'

area of a sector equation is: ???

A= 1/2r(squared)theta angle

A= ?

A= theta times radius squared/ divided by 2

angle(theta)= s/ ???

angle(theta)= s/r

circumference = ????

circumference= 2pie(radius) (one revolution) (theta angle is in radians)

number of revolutions= ?

number of revolutions= theta angle/2pie

radius= what speed

radius= linear speed/ angular speed

Cofunction Identities

sin (π/2 - x) = cos x cos (π/2 - x) = sin x tan (π/2 - x) = cot x pie/2 is 90 degrees cot (π/2 - x) = tan x x= theta angle sec (π/2 - x) = csc x csc (π/2 - x) = sec x

tan=

sin/cos

Unit Circle: what is sin and cos both at every 45 degrees (any number on the unit circle ending in either 15,25, 35, or 45)?

sin: square root of 2/2 cos: square root of 2/2 (positive or negative depending on which quadrant it is in)

Pythagorean Identities:

sin²∅ + cos²∅ = 1 tan²∅ + 1 = sec²∅ cot²∅ + 1 = cosec²∅

Unit Circle: what is the radians for all the 45 degrees (any number on the unit circle ending in either 15, 25, 35, or 45)?

some odd number (pie)/ 4

Unit Circle: what is the radians for every 90 degrees?

some odd number (pie)/2

Unit Circle: what is the radians every 30 degrees?

some odd number (pie)/6

Unit Circle: what is tan at every 60 degrees?

square root of 3 (positive or negative depending on which quadrant it is in)

Unit Circle: what is cos every 30 degrees in each quadrant?

square root of 3/2 (positive or negative depending on which quadrant it is in)

Unit Circle: sine at every 60 degrees

square root of 3/2 (will be positive or negative depending on what quadrant it is in)

Unit Circle: what is tan every 30 degrees?

square root of 3/3

S= ?

theta (degree/angle) times r (radius)

theta= number of revolutions (???)

theta= number of revolutions times (2pie)

Unit Circle: what is tan for every 90 degrees?

undefined

What is the linear speed formula?

v=s/t

What is the angular speed formula?

w= angle/t

Unit Circle: how do you find the specific degrees (30,45,60,90) ?

you go from the x axis (180 degrees, or 360 degrees, depending on which quadrant you're in) and count up or down from it (depending on what quadrant you're in) -example: if you have 150 degrees you do : 180-150= 30 degrees -example: if you have 315 degrees you do: 360-315= 45 degrees -example: if you have 240 degrees you do: 240- 180= 60 degrees